Differentiate the following w.r.t x Exercise 1.1
3)Differentiate the following w.r.t x :
(i)$(x^2+4x+1)^3+(x^3-5x-2)^4$
Solution-
$\frac{dy}{dx}=\frac{d}{dx}(x^2+4x+1)^3+(x^3-5x-2)^4$
=$\frac{d}{dx}(x^2+4x+1)^3+\frac{d}{dx}(x^3-5x-2)^4$
=$3(x^2+4x+1)\frac{d}{dx}(x^2+4x+1)+4(x^3-5x-2)\frac{d}{dx}(x^3-5x-2)$
=$3(x^2+4x+1)(2x+4)+4(x^3-5x-2)(3x^2-5)$
(ii)$(1+4x)^5(3x+x-x^2)^8$
(iii)$\frac{x}{\sqrt{7-3x}}$
(iv)$\frac{(x^3-5)^5}{(x^3+5)^3}$
(v)$\sqrt{cos x}+\sqrt{cos\sqrt{x}}$
(vi)$log(sec 3x+tan 3x)$
(viii)$\frac{1+sin x^{\circ}}{1-sin x^{\circ}}$
(ix)$cot\left(\frac{log x}{2}\right)$
(x)$\frac{e^{2x}-e^{-2x}}{e^{2x}+e{-2x}}$
(ix)$\frac{e^{\sqrt{x}}+1}{e^{\sqrt{x}}-1}$
(x)$\frac{e^{2x}-e^{-2x}}{e^{2x}+e^{-2x}}$
(xi)$log\left[ tan^3xsin^4x(x^2+7)\right]$
(xii)$log\left[\sqrt{\frac{1-cos3x}{1+cos3x}}\right]$
(xiv)$log\left[\sqrt{\frac{1+cos\frac{5x}{2}}{1+cos\frac{5x}{2}}}\right]$
(xv)$log\left[\sqrt{\frac{1-sinx}{1+sin0x}}\right]$
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| Differentiate following w.r.t x Exercise 1.1 |
$(x^2+4x+1)^3+(x^3-5x-2)^4$){kind=link}